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Mixing and the local central limit theorem for hyperbolic dynamical systems
Multi angle
Authors : Nándori, Péter (Author of the conference)
CIRM (Publisher )
37A50 - Relations with probability theory and stochastic processes
37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D50 - Hyperbolic systems with singularities (billiards, etc.)
60F05 - Central limit and other weak theorems
CIRM (Publisher )
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Abstract :
We present a convenient joint generalization of mixing and the local version of the central limit theorem (MLLT) for probability preserving dynamical systems. We verify that MLLT holds for several examples of hyperbolic systems by reviewing old results for maps and presenting new results for flows. Then we discuss applications such as proving various mixing properties of infinite measure preserving systems. Based on joint work with Dmitry Dolgopyat.
Keywords : mixing; local limit theorem; hyperbolic systems; dynamical systems; global mixing; Krickeberg-Hopf mixing
MSC Codes : Keywords : mixing; local limit theorem; hyperbolic systems; dynamical systems; global mixing; Krickeberg-Hopf mixing
37A50 - Relations with probability theory and stochastic processes
37D20 - Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D50 - Hyperbolic systems with singularities (billiards, etc.)
60F05 - Central limit and other weak theorems
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 15/11/2018 Conference Date : 01/11/2018 Subseries : Research talks arXiv category : Dynamical Systems Mathematical Area(s) : Dynamical Systems & ODE ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:56:15 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2018-11-01_Nandori.mp4 
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Information on the Event
Event Title : Probabilistic limit theorems for dynamical systems / Théorèmes limites probabilistes pour les systèmes dynamiquesEvent Organizers : Melbourne, Ian ; Pène, Françoise ; Volny, Dalibor Dates : 29/10/2018 - 02/11/2018 Event Year : 2018 Event URL : https://conferences.cirm-math.fr/1997.html
Citation Data
DOI : 10.24350/CIRM.V.19472103Cite this video as: Nándori, Péter (2018). Mixing and the local central limit theorem for hyperbolic dynamical systems. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19472103 URI : http://dx.doi.org/10.24350/CIRM.V.19472103 |
See Also
- [Multi angle] Levy diffusion of dispersing billiards with flat points / Author of the conference Zhang, Hong-Kun.
- [Multi angle] Diffusion limit for a slow-fast standard map / Author of the conference De Simoi, Jacopo.
- [Multi angle] Limit theorems for almost Anosov flows / Author of the conference Terhesiu, Dalia.
- [Post-edited] Growth of normalizing sequences in limit theorems / Author of the conference Gouëzel, Sébastien.
Bibliography
- Dolgopyat, D., & Nándori, P. (2017). On mixing and the local central limit theorem for hyperbolic flows.
